The export of certain Inuit sculpture from Canada to other parts of the world including the United States does have some restrictions. In order to reduce harvesting of marine animals such as whales and walruses, the United States Congress passed the Marine Mammal Protection Act in 1972. It was later modified in 1981 and a special section (101) of the act was developed to exclude Eskimo Inuit and other aboriginals living in the state of Alaska. Section 101 allowed Alaskan Natives to continue their traditions of hunting marine mammals for food and using parts of such animals as raw materials in the making of clothes, crafts and artwork.
The act makes it illegal for American citizens to import any ivory or whalebone from outside the United States. Therefore, American citizens would not be allowed to purchase any artwork containing ivory or whalebone from Canada and have it brought or shipped back to the United States.

However, the act as it stands allows American citizens to purchase similar artwork from Alaska since it is part of the United States. The export of such artwork created from marine mammals from the United States to Canada is not allowed.
Inuit sculpture containing whalebone, walrus or narwal tusks (both considered ivory) are restricted from import and export. However, Inuit sculpture containing caribou antler is allowed since caribou is not a marine mammal and therefore does not fall under this act.
Exporting Inuit sculpture containing whalebone or ivory from Canada to other international destinations will depend on each specific country as each has its own specific regulations.

Fines or penalties for importing or exporting illegal items can be very severe.
Fortunately, other forms of Inuit art such as stone or antler carvings and prints are not only able to be exported across the border, but are actually duty free.